MathDB

Let

m

and

n

be natural numbers with

mn

even. Jetze is going to cover an

m \times n

board (consisting of

m

rows and

n

columns) with dominoes, so that every domino covers exactly two squares, dominos do not protrude or overlap, and all squares are covered by a domino. Merlin then moves all the dominoe color red or blue on the board. Find the smallest non-negative integer

V

(in terms of

m

and

n

) so that Merlin can always ensure that in each row the number squares covered by a red domino and the number of squares covered by a blue one dominoes are not more than

V

, no matter how Jetze covers the board.

Problem Statement